Phys 102 – Lecture 7

1. Phys 102 – Lecture 7 Series and parallel circuits

2. Today we will... • Learn about electric circuits • Circuits with a battery, wires, and resistors • Circuits with a battery, wires, and capacitors • Analyze circuits • Take a complex-looking circuit like... • ...and turn into a simple-looking circuit like + +

3. Recall from last time... Electric potential difference across circuit element is its “voltage” Velement Should be “ΔV”, but we’ll usually drop the “Δ” + R C ε Batteries – pump charges Provide emf for charges Resistors – regulate current Dissipate power Capacitors – store charge Store energy Circuits connect elements with wires, which we treat as ideal conductors

4. Kirchhoff loop rule A charge making a complete loop around a circuit must return to the same electric potential (“height”) at which it started Resistor R (bumpy hill) + VR R + ε Battery (pump) ε Sum of electric potential differences (voltages) around circuit loop is zero

5. Series components Two components are said to be in series when they are connected end-to-end by a single wire R1 R1 I1 I2 + ε R2 V1 R2 ε V2

6. ACT: CheckPoint 1.2 Consider a circuit with two resistors R1 and R2 in series. Compare the voltages across the resistors: R1 = 1 Ω + ε R2 = 10 Ω V1 > V2 V1 = V2 V1 < V2

7. ACT: Capacitors in series Consider a circuit with two capacitorsC1 and C2 in series. Compare the voltages across the capacitors: C1 = 1 μF + ε C2 = 10 μF V1 > V2 V1 = V2 V1 < V2

8. Equivalent resistance & capacitance Circuit behaves the same as if series components were replaced by a single, equivalent component Resistors Capacitors I1 I2 Ieq C1 C2 Ceq Q1 –Q1 Q2 –Q2 Qeq –Qeq R1 R2 Req = = V1 V2 Veq V1 V2 Veq

9. Calculation: vascular resistance The circulatory system is analogous to an electric circuit Pressure difference Blood flow Vascular resistance emf Electric current Electrical resistance The circulatory system consists of different types of vessels in series with different resistances to flow εheart= 120 V* Vein Venule Capillary Arteriole Artery RV = 4 Ω Rv= 6 Ω Rc= 20 Ω Ra= 50 Ω RA = 20 Ω *Numbers represent accurate relative values

10. Calculation: vascular resistance Calculate the current I through the vascular circuit and the voltages across the different types of vessels εheart= 120 V εheart Simplify Vein Venule Capillary Arteriole Artery Expand RV = 4 Ω Rv= 6 Ω Rc= 20 Ω Ra = 50 Ω RA = 20 Ω Req

11. Kirchhoff junction rule Charges flowing through a junction split. By conservation of charge, the sum of currents into a junction equals the sum of currents out of a junction I2 I1 I2 I3 + + + + + + + Junction I3 I1 –

12. Parallel components Components are said to be in parallelwhen both ends are connected to each other, forming a loop containing only them I I2 I I2 I1 I1 + R1 R2 ε V2 V1 ε

13. ACT: Parallel or series? C2 ε Consider the circuit to the right. Which of the following statements is true? + C1 C4 C3 C1 & C4 are in series C2 & C4 are in parallel C1 & C3 are in parallel

14. ACT: Resistors in parallel Consider a circuit with two resistors R1 and R2 in parallel. Compare I1, the current through R1, to I2, the current through R2: + ε R1 = 1 Ω R2 = 10 Ω I1 > I2 I1 = I2 I1 < I2

15. ACT: CheckPoint 2.3 Now we add a switch S. What happens to the current out of the battery when the switch is closed? S + ε R1 R2 Ibattery increases Ibattery remains the same Ibattery decreases DEMO

16. Equivalent resistance & capacitance Circuit behaves the same as if parallel components were replaced by a single, equivalent component Capacitors Resistors C1 I1 I2 Ieq Q1 R1 –Q1 Q2 –Q2 Qeq –Qeq Ceq Req V1 V2 Veq V1 V2 Veq = C2 = R2

17. Calculation: vascular resistance In previous calculation, capillaric resistance accounts for ~20% of total vascular resistance, yet capillaries are the thinnest blood vessels, and should have the highest resistance. Why? Vein Artery Venule Arteriole Capillary

18. Calculation: cardiovascular system The human cardiovascular system consists of two circuits: pulmonary circulation which carries blood though the lungs, and systemic circulation which carries blood to the organs Rbrain Rpulm The organs of the body are connected in parallel in the systemic circuit + εheart Simple circuit model*: Rbody Rpulm = 12 Ω, Rbrain = 1 kΩ, Rbody = 160 Ω, εheart = 120 V *Numbers represent accurate relative values Calculate current through each component of circulatory system

19. ACT: analyzing circuits Which of the following circuit is different than the others? I II III + + + Circuit I Circuit II Circuit III All three are equivalent All three are different

20. Calculation: circulatory system Calculate current through each component of circulatory system Rpulm Rpulm = 12 Ω, Rbrain = 1 kΩ, Rbody = 160 Ω, εheart = 120 V Rpulm + + εheart εheart Simplify Simplify Rsyst Rtot εheart + Rbody Rbrain Rbrain & Rbodyare in parallel Rpulm & Rsystare in series

21. Calculation: circulatory system Calculate current through each component of circulatory system Rpulm = 12 Ω, Rbrain = 1 kΩ, Rbody = 160 Ω, εheart = 120 V Rpulm + + Expand εheart εheart Rtot Rsyst Rpulm & Rsystare in series

22. Calculation: circulatory system Calculate current through each component of circulatory system Rpulm = 12 Ω, Rbrain = 1 kΩ, Rbody = 160 Ω, εheart = 120 V Rpulm Rpulm + + + Expand Expand εheart εheart εheart Rbody Rbrain Rtot Rsyst Rbrain & Rbodyare in parallel

23. Summary of today’s lecture • Two basic principles: • Kirchhoff loop rule • Voltages around circuit loop sum to zero (based on conservation of energy) • Kirchhoff junction rule • Currents into a circuit branch equal currents out (based on conservation of charge)

24. Summary of today’s lecture • Series components Currents are the same Voltages add Resistors Capacitors • Parallel components Voltages are the same Currents add Resistors Capacitors • Don’t mix equations!